FERROMAGNETIC DISTORTION OF A WAVE 349 



component can be traced to the different axial slopes of the several 

 branches of the loop, caused by their different points of origination. 

 The slopes are fixed by the envelope of the magnetizing force; since 

 this envelope is periodic in the difference of the fundamental fre- 

 quencies, difference products will appear without corresponding sum 

 products in the induction. Such a phenomenon is a fundamental 

 property of the multivalued characteristic, and will occur wherever 

 the envelope of a complex wave is instrumental in selecting the branch 

 to be traversed. 



No simple yet general rule seems to embrace the behavior of the 

 various products in an iron core coil as governed by the amplitudes of 

 the fundamental currents. Each voltage component is proportional 

 to its frequency and to the product of two amplitudes, but these often 

 enter in a complicated way. For fundamental frequencies close to- 

 gether all the higher order voltages vary directly with the hysteretic 

 coefficient v, for widely separated frequencies the distortion may 

 depend also on the permeability through its effect on the axial slope 

 of the minor loops. At the extremes of the amplitude ratio certain 

 products or their components are found to be independent of one of 

 the fundamental currents, the stronger one in some instances. When 

 case 1 is applicable the third harmonic of the weaker fundamental 

 current is suppressed below the value it would have without the 

 stronger current superposed, while the third harmonic of the stronger 

 fundamental is affected only slightly by the presence of a second 

 frequency. Perusal of the table will disclose more detailed relations. 



Distortion Measured in Coils 



Voltages calculated by the theory have been compared with meas- 

 ured values for several coils using two common core materials. The 

 agreement found provides a check of the theoretical predictions. 



The two third order lower side frequencies of fundamental frequen- 

 cies P/Itt = 760 cycles per second and g/27r = 600 cycles per second 

 are plotted in Fig. 4 for a higher frequency current of ten milliamperes 

 in an iron dust coil of special design. The frequencies of the products 

 are 920 and 440 cycles per second. These data w^ere taken by I. E. 

 Wood and the calculations were made by A. G. Tynan. These curves 

 show the product as a function of the amplitude ratio more directly 

 than the curves of Fig. 3. 



Both upper and lower third order side frequencies have been meas- 

 ured by A. G. Landeen. The results are given in Figs. 5 and 6 for an 

 annular core of iron dust. It is so wound that the magnetizing force 

 is 0.04 times the current in milliamperes. The figures show two third 



